TY - JOUR

T1 - A phase-space beam summation formulation for ultrawide-band radiation

AU - Shlivinski, Amir

AU - Heyman, Ehud

AU - Boag, Amir

AU - Letrou, Christine

N1 - Funding Information:
Manuscript received November 21, 2001; revised June 12, 2003. The work of E. Heyman was supported in part by the Israel Science Foundation under Grant 216/02 and in part by the Air Force Office of Scientific Research (AFOSR) under Grant F49620-01-C-0018. The work of A. Boag was supported in part by the Israel Science Foundation under Grant 577/00. A. Shlivinski was with the School of Electrical Engineering, Tel Aviv University, Tel Aviv 69978, Israel. He is now with the Department of Electrical Engineering, University of Kassel, 34109 Kassel, Germany. E. Heyman and A. Boag are with the School of Electrical Engineering Tel Aviv University, Tel Aviv 69978, Israel. C. Letrou is with GET/INT, CNRS SAMOVAR, UMR 5157, France. Digital Object Identifier 10.1109/TAP.2004.832513

PY - 2004/1/1

Y1 - 2004/1/1

N2 - A new discrete phase space Gaussian beam (GB) summation representation for ultrawide-band (UWB) radiation from an aperture source distribution is presented. The formulation is based on the theory of the windowed Fourier transform (WFT) frames, wherein we introduce a novel relation between the frequency and the frame overcompleteness. With this procedure, the discrete lattice of beams that are emitted by the aperture satisfies the main requirement of being frequency independent, so that only a single set of beams needs to be traced through the medium for all the frequencies in the band. It is also shown that a properly tuned class of iso-diffracting (ID) Gaussian-windows provides the "snuggest" frame representation for all frequencies, thus generating stable and localized expansion coefficients. Furthermore, due to the ID property, the resulting GBs propagators are fully described by frequency independent matrices whose calculation in the ambient environment need to be done only once for all frequencies. Consequently, the theory may also be expressed directly in the time-domain as will be presented elsewhere. The localization implied by the new formulation is demonstrated numerically for an UWB focused aperture. It is shown that the algorithm extracts the local radiation properties of the aperture source and enhances only those beams that conform with these properties, i.e., those residing near the phase space Lagrange manifold. Further localization is due to the fact the algorithm accounts only for beams that pass within a few beamwidths vicinity of the observation point. It is thus shown that the total number of beams is much smaller than the Landau Pollak bound on the aperture's degrees of freedom.

AB - A new discrete phase space Gaussian beam (GB) summation representation for ultrawide-band (UWB) radiation from an aperture source distribution is presented. The formulation is based on the theory of the windowed Fourier transform (WFT) frames, wherein we introduce a novel relation between the frequency and the frame overcompleteness. With this procedure, the discrete lattice of beams that are emitted by the aperture satisfies the main requirement of being frequency independent, so that only a single set of beams needs to be traced through the medium for all the frequencies in the band. It is also shown that a properly tuned class of iso-diffracting (ID) Gaussian-windows provides the "snuggest" frame representation for all frequencies, thus generating stable and localized expansion coefficients. Furthermore, due to the ID property, the resulting GBs propagators are fully described by frequency independent matrices whose calculation in the ambient environment need to be done only once for all frequencies. Consequently, the theory may also be expressed directly in the time-domain as will be presented elsewhere. The localization implied by the new formulation is demonstrated numerically for an UWB focused aperture. It is shown that the algorithm extracts the local radiation properties of the aperture source and enhances only those beams that conform with these properties, i.e., those residing near the phase space Lagrange manifold. Further localization is due to the fact the algorithm accounts only for beams that pass within a few beamwidths vicinity of the observation point. It is thus shown that the total number of beams is much smaller than the Landau Pollak bound on the aperture's degrees of freedom.

UR - http://www.scopus.com/inward/record.url?scp=4344560361&partnerID=8YFLogxK

U2 - 10.1109/TAP.2004.832513

DO - 10.1109/TAP.2004.832513

M3 - Article

AN - SCOPUS:4344560361

VL - 52

SP - 2042

EP - 2056

JO - IEEE Transactions on Antennas and Propagation

JF - IEEE Transactions on Antennas and Propagation

SN - 0018-926X

IS - 8

ER -